A spacecraft of negligible mass is placed in a circular parking orbit above Earth’s…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A spacecraft of negligible mass is placed in a circular parking orbit

400\,\text{km}

above Earth’s surface. Use the data

M_{E}=6.0\times10^{24}\,\text{kg}

R_{E}=6.4\times10^{6}\,\text{m}

and

G=6.67\times10^{-11}\,\text{N m}^2\!\text{/kg}^2

. (a) Calculate the minimum speed (relative to Earth) that must be imparted to the spacecraft at this altitude so that it can escape Earth’s gravitational field. (b) The escape speed at Earth’s surface is about

11.2\,\text{km s}^{-1}

. By what percentage is the speed found in part (a) lower than this surface value?

Related theory

Universal Law of Gravitation
Gravitation
Escape Velocity
Escape speed

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